The Imp in a Bottle: Ponzi/Madoff in a Broader Perspective

Less than two months ago, Bernard Madoff was arrested by the FBI for securities fraud. Given the relative amounts of money involved and pain inflicted, Ponzi schemes should perhaps henceforth be called Madoff schemes.

Whatever their outward appearance, almost all such scams involve collecting money from an initial group of investors by promising them solid and sometimes extraordinary returns. The returns to the initial group come from money contributed by a larger secondary group of people. A still larger group of people contributes to both of the smaller earlier groups, and so on.

This burgeoning process continues for a while, but the number of people needed to keep the pyramid growing and the money coming in increases exponentially and soon becomes difficult to maintain. People drop out, and the easy marks become scarcer. The system collapses under its own weight when enough new people can no longer be found.

Dot-Coms, Mortgages, Our Genes and the Environment

The logic is clear, but the situation gets more interesting when many people are suspicious of the scheme or even aware of its fraudulence (as they were not with Ponzi or Madoff). In this case they generally worry only about what happens one or two steps ahead and may anticipate being able to get out before a collapse. That is, one may find it rational to buy into such an unsavory scheme if one is confident of recruiting a "bigger sucker" as a replacement.

The dot-coms' meteoric stock price rises in the late '90s and their subsequent precipitous declines in 2000 and 2001 were attenuated versions of the same general sort of scam. There was a degree of knowingness among some investors about the unsustainability of the boom. They tried to get in on the initial public offering, hold on as the stock rocketed upward, and jump off before it plummeted.

Thanks to complicated derivatives and other opaque financial instruments, the recent collapse in the housing market and the more general financial crisis it has precipitated have an even more repellent aroma to them, if I may Ponzificate a bit.

While corporate venality and fraud certainly played a role in some of these precipitous declines, the collapses of the various dot-coms, banks, foundations and financial institutions were not primarily the fault of con artists and high-society lowlifes. The responsibility extends far wider. Even when investors recognized bubbles (or outright swindles) for what they were, most figured, usually incorrectly, that they'd be able to find a chair when the mania-inducing music stopped.

Maybe our genes are to blame. (They always seem to get the rap.) Natural selection no doubt favors organisms that respond to local or near-term events and ignore distant or future ones, which are discounted in somewhat the same way that future money is. We want tasty food now regardless of distant health consequences.

The ravaging of the environment also may be seen as a kind of unintentional global Ponzi scheme. The early "investors" (the beneficiaries of the fossil fuels, rapid deforestation, water and air pollution, etc.) did well, later ones have fared less well, and a catastrophe may wipe out all "investment gains."

The Imp in the Bottle

A quite different illustration of our short-sightedness comes courtesy of Robert Louis Stevenson's "The Imp in the Bottle." The story tells of a genie in a bottle able and willing to satisfy your every romantic whim and financial desire. You're offered the opportunity to buy this bottle and its amazing denizen at a price of your choice. There is a serious limitation, however.

When you've finished with the bottle, you have to sell it to someone else at a price strictly less than what you paid for it. If you don't sell it to someone for a lower price, you will lose everything and will suffer excruciating and unrelenting torment. What would you pay for such a bottle?

Certainly you wouldn't pay 1 cent because then you wouldn't be able to sell it for a lower price. You wouldn't pay 2 cents for it either since no one would buy it from you for 1 cent since everyone knows that it must be sold for a price less than the price at which it is bought. The same reasoning shows that you wouldn't pay 3 cents for it since the person to whom you would have to sell it for 2 cents would object to buying it at that price since he wouldn't be able to sell it for 1 cent. Likewise for prices of 4 cents, 5 cents, 6 cents, and so on.

We can use mathematical induction to formalize this argument, which proves conclusively that you wouldn't buy the genie in the bottle for any amount of money. Yet you would almost certainly buy it for 1,000 dollars. I know I would. At what point does the argument against buying the bottle cease to be compelling?

The question is more than academic since in countless situations people prepare exclusively for near-term outcomes and don't look very far ahead. They myopically discount the future at an absurdly steep rate.

On the other hand, in certain quite different circumstances this tendency can also be seen as a rationally exuberant "seize the day" mentality that has much to recommend it. Live large before the music stops ... but be a little skeptical.

John Allen Paulos, a professor of mathematics at Temple University, is the author of the best-sellers "Innumeracy" and "A Mathematician Reads the Newspaper," as well as "Irreligion: A Mathematician Explains Why The Arguments for God Just Don't Add Up." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.

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